During heating-up and cooling-down processes, as occur in component walls, for example in a steam turbine, a valve housing or a steam line, in particular when changing the operating mode, temperature gradients are produced in thick walls of these components and may lead to considerable material stresses. These material stresses may lead to premature material wear to the extent that cracks form.
To monitor such temperature gradients specifically in the case of applications in steam power plants, previously at least one or more temperature measuring points were incorporated in the component wall. Measured values determined for the temperature of the wall and the temperature of the working medium can be used to estimate temperature differences within the component wall and in particular to determine the assigned average integral wall temperature. Comparison of the average integral temperature with permissible limit values makes it possible to keep the thermal material stresses within permissible limits. However, this method is comparatively cost-intensive and error-prone.
Alternatively, the average integral wall temperature can also be calculated without the need for costly and error-prone measuring points incorporated in the wall or in the case of components which cannot be provided with a measuring point (for example a turbine shaft). One possible method is to calculate this temperature by means of a mathematical substitute model, in particular on the basis of the Bessel equation, for the heat conduction in a metal rod. However, systems previously realized on this basis in the instrumentation and control of industrial plants, such as for example tubes of steam power plants, have a tendency to undergo oscillations, dependent on the period of the temperature changes of the working medium, which limit reliable assessment of the temperature values obtained in such a way.